(Computer) Theorem Proving (TP) is becoming a paradigm as well as a
technological base for a new generation of educational software in
science, technology, engineering and mathematics. The ThEdu'17
workshop brings together experts in automated deduction with experts
in education in order to further clarify the shape of the new
software generation and to discuss existing systems.

These words introduced the
ThEdu'17 workshop
associated to CADE26, 6 Aug 2017, Gothenburg, Sweden. ThEdu'17 was a
vibrant workshop, with one invited talk and eight contributions. It
triggered the post-proceedings at hand.

ThEdu'17 is the 6th edition of the ThEdu series of workshops. The
major aim of the ThEdu workshop series was
to link developers interested in adapting TP to needs of education and
to inform mathematicians and mathematics educators about TP's
potential for educational software--together with a parallel workshop
series in the Conference on Digital Tools in Mathematics Education
(CADGME)
conferences, primarily addressing educators responsible for STEM
(Science, Technology, Engineering
and
Mathematics) studies. Looking back to
seven years of the parallel workshop series shows that the "new
TP-based generation" is gaining acceptance in a wider public, that
ideas about specific use of TP technologies prosper and that envisaged
applications address an increasing range of issues.

The contributions to ThEdu are diverse reflecting the communities the
authors come from. ThEdu's program committee reflects this diversity,
too. Collaboration between these communitiesis required to path the
way towards the new generation mentioned above. So we face this
diversity as positive, making the break lines explicit in the survey
on contributions below--indicating referees' objections.

Schreiner et al. presented a specification language plus automated
(conter-)example generation as the basis of a tool chain already well
established in education--and were criticised for lack of educational
experience with the basis of the chain. On the other hand, Böhne
et al. presented empirical research about academic education in
proving based on a mini-adaption of Coq--and were criticised for
bypassing recent systems' features of structured proof and for
disregarding their usability in education. Villadsen et al. presented
a comprehensive substitution for Isabelle's front-end (while keeping
the logical background transparent) in order in improve educational
use--and were confronted with a detailed description how Isabelle "as
is" can be used for the same educational purpose.

Using an opposite approach, three contributions even start building a
TP from scratch for educational purposes--with objections from the
point of logical trustability as well as from "re-inventing the
wheel", see "Isabelle: The
Next 700 Theorem Provers". The three respective technological
bases are different: Leach-Krouse presents a Haskell-based
implementation generic for various kinds of "baby" provers. Ehle et
al. focus sequent calculus and base their implementation on Java.
Frank et al. focus untyped lambda calculus as a starting point for a
logical framework even incorporating ITP (and base their
implementation on C++).

Geometry is an exercise field for learning to prove, in particular in
Anglo-American countries. Two contributions act on this relevance and
provide respective software support: Quaresma et al. presented a new
connection between an e-learning platform and a repository of geometry
problems for theorem provers plus a wealth of ideas for exploitation
in education--and were criticised that their paper reads more like a
research proposal rather than a publishable description of research
results (in terms of technology). Richard et al. build an inference
engine in Prolog from scratch, which is considered more efficient than
adaption of existing TPs, given the restricted problem space in
geometry education--and were criticised for limited functionality
inhibiting transition to higher levels of education.

One contribution not even mentions "proof": Krempler et al. use
Isabelle's components to support "engineering mathematics" by
interactive formal specification and subsequent step-wise construction
of solutions (where the latter is forward proof using a specific
format).

So there are good reasons for criticism from both sides, from the side
of TP as well as from the side of education. The PC invested much
effort to balance the two sides and to ensure quality of contributions
appropriate to EPTCS.

The small collection of papers in this volume makes a colourful carpet
of various ideas and divergent processes--divergent not only
alongside the two communities brought together by the workshop series,
but even within these communities. That is the present picture in the
interdisciplinary approach to the novel challenge posed by ThEdu's
call. It's ultimate aim, improvement of software support in learning
mathematics, will require collaboration. Such collaboration is not in
sight of the present collection.

The PC hopes that this publication will increase mutual
understanding between the two sides and attract new researchers from
several communities in order to enhance existing educational software
as well as study of new software developments. The PC invites all
readers to the ThEdu'18 edition, associated to FLOC, Oxford, UK, 6-19
July 2018.